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In silico assessment of the effects of various compoundsin MEA/hiPSC-CM assays: Modelling and numerical

simulationsEmanuela Abbate, Muriel Boulakia, Yves Coudière, Jean-Frédéric Gerbeau,

Philippe Zitoun, Nejib Zemzemi

To cite this version:Emanuela Abbate, Muriel Boulakia, Yves Coudière, Jean-Frédéric Gerbeau, Philippe Zitoun, et al..In silico assessment of the effects of various compounds in MEA/hiPSC-CM assays: Modelling andnumerical simulations. Journal of Pharmacological and Toxicological Methods, Elsevier, 2018, 89,pp.59-72. hal-01562673

In silico assessment of the effects of various compounds

in MEA/hiPSC-CM assays: Modelling and numerical

simulations

E. Abbate, M. Boulakia, Y. Coudiere, J-F. Gerbeau, P. Zitoun and N.Zemzemi

Abstract

We propose a mathematical approach for the analysis of drugs effects onthe electrical activity of human induced pluripotent stem cell-derived car-diomyocytes (hiPSC-CMs) based on multi-electrode array (MEA) experi-ments. Our goal is to produce an in silico tool able to simulate drugs actionin MEA/hiPSC-CM assays. The mathematical model takes into account thegeometry of the MEA and the electrodes’ properties. The electrical activityof the stem cells at the ion-channel level is governed by a system of ordi-nary differential equations (ODEs). The ODEs are coupled to the bidomainequations, describing the propagation of the electrical wave in the stem cellspreparation. The field potential (FP) measured by the MEA is modeled bythe extra-cellular potential of the bidomain equations. First, we propose astrategy allowing us to generate a field potential in good agreement with theexperimental data. We show that we are able to reproduce realistic fieldpotentials by introducing different scenarios of heterogeneity in the actionpotential. This heterogeneity reflects the differentiation atria/ventricles andthe age of the cells. Second, we introduce a drug/ion channels interactionbased on a pore block model. We conduct different simulations for five drugs(mexiletine, dofetilide, bepridil, ivabradine and BayK). We compare the sim-ulation results with the field potential collected from experimental measure-ments. Different biomarkers computed on the FP are considered, includingdepolarization amplitude, repolarization delay, repolarization amplitude anddepolarization-repolarization segment. The simulation results show that themodel reflect properly the main effects of these drugs on the FP.

Keywords: Cardiac electrophysiology, MEA, field potential, drugmodelling, hIPSC-CMs.

Preprint submitted to Elsevier July 16, 2017

1. Introduction

Recent studies on stem cells showed that it is possible to induce pluripo-tency, i.e. the capability of differentiating into all tissues of an organism [1].Stem cell-derived cardiomyocytes (CMs) appear as a promising tool in re-generative medicine, for example to restore the cardiac function after aninfarct [2, 3].

Human induced pluripotent stem cells (hiPSCs) are considered in thiswork. These cells are derived by reprogramming somatic cells and can becultivated in the pluripotency state or differentiated into somatic cell types,including CMs [4]. Until now, the knowledge regarding the cardiac tissuemainly relied on animal models, like dog, rabbit or guinea pig. Today, manytypes of human pluripotent stem cells are investigated for their potential toproduce functional CMs [5, 6]. hiPSC-CMs are valuable models because oftheir resemblance to adult myocytes, especially in the electrophysiological be-havior [7]. Therefore, the role of hiPSC-CMs as in vitro models is becomingmore and more important. In hiPSC-CMs preparations, a strong heterogene-ity in the morphology of the action potentials is usually observed. However,the signals can be classified into three major types: nodal-like, embryonicatrial-like, and embryonic ventricular-like [5, 4].

The hiPSC-CMs have been used in different fields: toxicity testing, studyof certain diseases, pharmacological response, drug design etc. [6, 4, 8, 9, 10,11]. The present study is related to the problem of drug screening in safetypharmacology. Our goal is to model and simulate MEA measurements thatare performed by pharmaceutical companies on hiPSC-CMs preparations.The aim of these experiments is to predict and test the main effects of a drugon the electrophysiology of cardiomyocytes. But the electrical signal collectedby an MEA device, called the Field Potential (FP), is difficult to analyze,because of its variability, and because it has been much less studied than theAction Potential (AP). With this study, we want to show that mathematicalmodeling and numerical simulation can contribute to a better understandingof the MEA measurements. Some preliminary simulations of the FP wererecently presented [12, 13, 14] and the modeling of drug effects, side effectsand interactions was addressed in several works [15, 16, 17]. But to the bestof our knowledge, the present article is the first in silico study of drug effectson the FP.

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Here is a brief description of the methods adopted in this work. Our math-ematical model is based on the bidomain equations, used in many works forthe description of the electrical activity of the heart. In order to reproducethe electrical activity of hiPSC-CMs, a state-of-the-art ionic model describ-ing the membrane activity of stem cells is used in Paci et al [18]. Since theexperimental measurements are registered by MEA devices, a model of elec-trodes is introduced and coupled to the bidomain equations. The resultingequations allow us to model the field potential recorded by the MEA device.A specific device is considered (the 60-6 well MEA produced by the companyMulti Channel Systems) but the methodology can be applied to other kindsof MEAs. This device is made of six independent wells. Each well containsnine electrodes (Fig. 1(a)). Six independent experiments can thus be donewith identical surrounding conditions at once [19].

(a) MEA with 6 wells (b) Well with 9 electrodes

Figure 1: Multichannel Systems device [19]. Panel (a): 60-6well MEA device. Panel (b):zoom on one well with the 9 electrodes (reproduced with permission).

The geometry used for the computation is two-dimensional. It modelsone layer of cells in a well, as represented in Fig. 1(b). A special effort isdedicated to the modeling of the electrophysiological heterogeneity, whichis a prominent characteristic of hiPSC-CMs preparations. This is done byintroducing different phenotypes, atrial- and ventricular-like, and by vary-ing the action potential amplitudes. Various configurations are generatedfollowing this approach. The in silico results corresponding to the differentconfigurations are averaged and compared to in vitro experiments for fivedifferent drugs (mexiletine, dofetilide, bepridil, ivabradine and BayK).

The paper is organized as follows. In Section 2, the mathematical modelsof the field potential and the drug-channel interactions are presented. In Sec-

3

tion 3, the simulation results are presented and compared with experimentalmeasurements. Section 4 is dedicated to a discussion and some concludingremarks.

2. Materials and Methods

In this section, the methodology of the study is detailed. First, a math-ematical model is presented to reproduce the experimental field potential insilico. Then a strategy is proposed to reflect the strong variability observedin the experiments. The section ends with the approach used to model theaction of compounds on the ion channels.

(a) Electrodescircuit

(b) Domain (c) Mesh

Figure 2: Schematic representation of the electrodes electrical circuit (a). 2D domain Ωwith dimensions and positions of the 9 electrodes (b). Computational mesh representinga triangular discretization of the domain Ω with h ≈ 25µm (c).

2.1. Electrophysiology of a monolayer of cells in a MEA

Since the culture of hiPSC-CMs is made of a monocellular layer, with athickness zthick much smaller than the other dimensions, the domain occupiedby the cells in a well is assumed to be two-dimensional (Fig. 1(b)). It isdenoted by Ω and is schematically represented in Fig. 2(b).

The electrical activity of the tissue is described using the bidomain equa-tions, which result from the homogenization of a microscopic model thattakes into account both the intracellular and the extracellular media. For a

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detailed derivation of the bidomain model see for example [20, 21]. In thetwo-dimensional configuration of the MEA, these equations read:

AM

(CM

∂VM∂t

+ Iion

)− div (σI∇VM)− div (σI∇ue) = AMIstim in Ω(1a)

−div ((σI + σE)∇ue)− div (σI∇VM) =1

zthick

∑ek

Ikel|ek|

χek in Ω. (1b)

dw

dt− g (VM ,w) = 0 in Ω. (1c)

where |ek| denotes the surface of the electrode k, and χek denotes its char-acteristic function, i.e. the function equal to one inside the electrode andzero outside. Functions VM and ue are respectively the transmembrane andextracellular potentials. The constant CM is the transmembrane specific ca-pacitance, AM is the surface area of membrane per unit volume of tissue,σI and σE are respectively the intracellular and extracellular conductivities.The transmembrane ionic current Iion is provided by the model proposed inPaci et al [18]. This ionic model, based on the Hodgkin-Huxley theory [22]and represented by Equation (1c), reproduces the activity of auto-excitablehiPSC-CMs. It includes the activity of several transmembrane channels andthe intracellular calcium exchanges. The state variables vector w consists ofthe concentrations of ions and the gate variables. The precise definition offunction g(VM ,w) can be found in the appendix of [18]. In Equation (1a),the current Istim is an external stimulation, which can be applied at a certainlocation of the domain for a certain duration. For the boundary conditionsof the coupled problem, we impose that the flux of the intracellular potential(VM + ue) over the boundary is equal to zero

σI∇(VM + ue) · n = 0.

For the extracellular potential, we use homogeneous Dirichlet boundary con-ditions (ue = 0) on three edges connected to the ground, which has a ”U”shape as shown in Fig1(b). For the remaining edge, we use a non flux bound-ary condition σE∇ue · n = 0.

Let us now explain the source term added in Equation (1b) to model thepresence of the electrodes. In a three-dimensional description, the followingboundary condition should be introduced in the regions where the electrodes

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are located [23]:

σE∇ue · n =Ikel|ek|

on ek, (2)

where Ikel is the electric current measured by the kth electrode and computedusing the electric model of Fig. 2(a), by solving the following ODE:

dIkeldt

+Ikelτ

=Cel

τ

dUk

dtwith Uk =

1

|ek|

∫ek

ue dek, (3)

where τ = (Ri + Rel)Cel, Ri standing for the ground resistance, Rel and Cel

for the resistance and the capacitance of the electrode. In Eq. (3) we haveintroduced Uk as the mean value of the extracellular potential ue over theelectrode k.

Since the thickness of the monolayer of cells zthick is supposed to be verysmall compared to the other dimensions of the problem, we assume that allthe variations along the z-direction are negligible compared to the variationsalong the directions x and y. After some manipulations, condition (2) of thethree-dimensional problem is transformed into the source term in the two-dimensional equation (1b). The field potential measured by electrode k isthen computed as

Ukfp = RiI

kel.

In Table 1, we provide the values of the macroscopic model parametersused in the simulations. For the tissue conductivity, we choose the valuesσi = 10µS cm−1 and σe = 30µS cm−1, in order to fit with the conductionvelocity in the experimental data. These values are lower than conductivitiesin human cardiac tissue, due to the fact that in hiPSC-CMs the conductionvelocity (CV) is much solwer than in the human heart [6]. The CV obtainedwith the chosen conductivities is around 4cm/s. For the electrode model, wetake a ground resistance Ri = 109Ω and an electrode resistance of Rel = 106Ω.Rel was not introduced in the model provided in [23]. We introduce it in orderto model as close to reality as possible the physical phenomena. Nevertheless,according to equation (3), the resistance Rel does not have any effect on thefield potential since Ri = 109Ω >> Rel. In [23], the authors prove that takingground resistance values of 1012Ω and of 109Ω gives the same accuracy as aperfect electrode with infinite resistance. The value of Cel is in the range ofmanufacturer values provided in [23].

The system of partial differential equations is discretized in space withpiecewise linear finite elements, and in time with a time stepping scheme [24].

6

We use a triangular mesh as shown in Figure 2(c). The full time and spacenumerical discretizations are given in the supplementary material, wherewe also provide a time convergence analysis. We have chosen the value of∆t = 0.2 ms in order to ensure a relative error lower than 1% on the actionpotential. The reference solution in this convergence analysis is obtainedusing a time step ∆t = 1µs.

Parameter Symbol ValueRate of membrane surface per volume [25] AM 1200 cm−1

Membrane specific capacitance [25] CM 1 µF cm−2

Intracellular conductivity σI 10 µS cm−1

Extracellular conductivity σE 30 µS cm−1

Electrodes capacitance [23] Cel 10−10 FElectrodes ground resistance [23] Ri 109 ΩElectrodes internal resistance Rel 106 Ωz thickness zthick 10−4 cm

Table 1: Values of the parameters used in the simulations.

In Figure 3, we plot the time course of the simulated field potential forthe 9 electrodes. The tissue was stimulated at the bottom-left corner withIstim = 150A/cm−2. In this case, if we do not stimulate the tissue, all cellsdepolarize at the same time. The extra-cellular potential solution would thenbe equal to zero in the whole domain and the computed FP would also beequal to zero.

Figure 3: Simulated field potentials over the 9 electrodes for ventricular-like hiPSC-CMwithout introducing any heterogeneity in the model.

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2.2. Handling the heterogeneity and the variability

2.2.1. Experimental observations and main hypotheses

The electrophysiological heterogeneity and variability are a prominentcharacteristic of stem cell preparations, as pointed out in different works [4,6, 8, 26]. The heterogeneous behavior mainly comes from the intrinsic dif-ferences in the cell lines used in experiments and from the conditions underwhich the cells are differentiated. Patch-clamp measurements suggest a clas-

Figure 4: Field potential signals of the 9 electrodes recorded from one MEA well. Theexperimental measurements were produced by Janssen / NMI and provided by Notocord.

sification of the cells among three main phenotypes; atrial-, ventricular- andnodal-like. This classification is based on the comparison of their AP withadult cardiomyocytes’ AP. Distinction between atrial and ventricular-like isusually based on the following biomarker [4, 6]:

RO =APD30−40

APD70−90

≤ 1.5 atrial-like

> 1.5 ventricular-like,

where APD stands for action potential duration. This ratio measures theslope at the beginning of repolarization. A triangular shaped AP is classi-fied as atrial-like. But still inside a phenotype, we observe large variationsin the AP morphologies. For instance in [4], the variations of biomarkerssuch as AP amplitude, firing velocity and APD90 inside each phenotype arestudied and quantified. In a MEA well, the field potential signals collectedby the electrodes at different locations are different in shape and behavior.

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Figure 5: In vitro data: Panel (a): field potential signals of 6 MEA wells (each one with9 electrodes). Zoom on electrode number one (c)

For instance, Fig. 4 shows the 9 experimental FPs in a MEA well: shapedifferences are striking. In Fig. 5(a), the results of a MEA experiment arepresented: in the same environment conditions, the signals collected in thesix wells exhibit great differences in amplitude, shape and frequency.

The in silico signals given by the model (1a)-(3) are reported in Figure 3are not in a good agreement with the experimental signals. Conjecturingthat the discrepancy is due to the absence of heterogeneity in the in silicomodel, we will enrich our model with some new features detailed in the nextsubsections.

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2.2.2. Modeling different phenotypes

In [18], the authors propose atrial- and ventricular-like ionic models: themain differences concern some channels conductances and the ICaL dynam-ics, which is the main responsible for the plateau phase. As a first attempt atmodeling the electrophysiological heterogeneity, we introduce the two pheno-types in the same hiPSC-CMs preparation. The original domain is split intotwo different parts, as in the simple configuration of Fig. 6: Ω = Ω1 ∪ Ω2.Ventricular-like cells being the predominant phenotype [4], the ventricularmodel is solved in Ω1 and the atrial model in Ω2. As will be shown in Sec-

Figure 6: Splitting of the domain Ω into two different regions Ω1 and Ω2.

tion 3, this strategy is not sufficient to qualitatively match the experimentalsignals, especially during the plateau phase. Recalling that the presence oftwo phenotypes mainly affect the slope at the end of the plateau and duringthe repolarization, we hypothesized that further heterogeneities should beincluded in the in silico experiments, in particular in the AP amplitude andin the plateau phase.

2.2.3. Transmembrane potential rescaling

According to the experimental measurements of Fig. 5, the interval be-tween depolarization and repolarization is almost never flat and varies a lotamong the different signals. We noticed that this behavior could be repro-duced by creating a difference in the peak and in the plateau phase of theAPs in different parts of the monolayer of cells. We rescale the transmem-brane potential VM : this way a gradient is encountered by the electrotoniccurrent. The study by the Antzelevitch group [4] shows that the amplitudeof the AP can vary from the registered mean value. The standard deviationof this variation is around 25% of the mean value of the amplitude in each

10

phenotype. We include this experimental evidence in the model by rescal-ing the transmembrane potential VM in one or more parts of the domainΩ. Because of the absence of a detailed description of how the different cellphenotypes are distributed in the experiment, we try different repartitions.To understand the effect of the heterogeneities in that AP magnitude, westart with a simple splitting of the domain. As shown in Fig. 6, our goalis to simulate an action potential with a sufficiently high spatial gradient atthe plateau phase, allowing to reproduce FPs with the same shape as theexperimental signals. If we denote by Vrest the resting potential of the Pacimodel and take 0 < c1 < 1 and c2 = (1 − c1)Vrest, by solving the followingzero-D models

AM

(CM

dV1dt

+ Iion (V1,w1, t)

)= 0

dw1

dt= g (V1,w1, t) ,

(4)

AM

(CM

dV2dt

+ c1Iion

(1

c1(V2 + c2),w2, t

))= 0

dw2

dt= g

(1

c1(V2 + c2),w2, t

).

(5)

we obtainV2 = c1V1 − c2 and w1 = w2. (6)

Since the standard deviation of the action potential magnitude variation isaround 25% of the mean value of the amplitude in each phenotype [4], inwhat follows we will take 0.7 ≤ c1 ≤ 1. By splitting the domain Ω intotwo regions Ω1 and Ω2 as described in Fig. 6, we introduce the rescalingheterogeneity in the bidomain model as follows

AM

(CM

∂VM∂t

+ Iion (VM ,w1, t)

)− div (σI∇ (VM − ue)) = AMIstim in Ω1

dw1

dt= g (VM ,w1, t) in Ω1

AM

(CM

∂VM∂t

+ c1Iion

(1

c1(VM + c2),w2, t

))− div (σI∇ (VM − ue)) = AMIstim in Ω2

dw2

dt= g

(1

c1(VM + c2),w2, t

)in Ω2.

(7)

11

Equations (1a) and (1c) are replaced by the systems of equations (7). Theelectrotonic current introduced by the diffusion terms will avoid the discon-tinuity in the transmembrane potential at the interface between Ω1 and Ω2.

2.2.4. Arrangement in clusters

The splitting in two domains presented in Fig. 6 is clearly arbitrary. Herewe consider other kinds of cell arrangements giving results which are also ingood qualitative agreement with the experiments. The underlying ideas is togenerate many different plausible configurations from which it will be possibleto do statistics. This strategy allows us to limit the impact of arbitrarychoices of cells distribution and can be a good way to circumvent the absenceof information about the cell variability and heterogeneity in each well. A10 × 10 grid of squares (ωi)i=1,...,100 is introduced in Ω. Let I1 and I2 bea partition of the set 1, . . . , 100. Each ωi is assigned to one of the twosubdomains introduced in Eq. (6): Ω1 := ∪i∈I1ωi and Ω2 := ∪i∈I2ωi. LetF be the fraction of domain Ω where the rescaling is employed, namelyF := |Ω2|/|Ω| (| · | stands for the surface measure). We keep F = 20% and werandomly change the spatial arrangement of Ω1 and Ω2 for every simulation.Two classes of configuration are considered: the “clustered” configurations,when Ω2 is a big connected part, and the “scattered” configurations, when Ω2

is scattered into multiple small subdomains. Examples of such configurationsare given in Fig. 11.

2.2.5. Reproducing the field potential variability

Given the variability observed in the experiments (see e.g. the measure-ments for 6 different wells in Fig. 5(a)) and the uncertainties of the model,the exact in silico reproduction of a specific experiment would not makemuch sense. Instead, we propose to consider several scenarios and computeaverages and standard deviations of quantities of interest. We indicate inthis section how the scenarios are elaborated. In the subsections 2.2.2 and2.2.3, two ways of reproducing the shape heterogeneity of the signals mea-sured from hiPSC-CMs preparations have been investigated: the introduc-tion of two phenotypes (atrial and ventricular types) and the introductionof a rescaling in the AP amplitude. We will use these two tools to generatevarious configurations. To do so, the domain is split as Ω = Ω1 ∪ Ω2 and weconsider in Ω1 a ventricular model with a rescaling while in Ω2 we consideran atrial model. The splitting is performed by favoring clustered configura-

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tions. The ventricular-like transmembrane potential is rescaled because theAP amplitude of ventricular cells is lower, in average, than the one of atrialcells [4]. Following the experimental results in [4] and taking to account thematurity and phenotype heterogeneities, we set the parameters c1 and c2 inorder to reduce the magnitude of the AP by about 30% in Ω2.

2.3. Model for the drug/ion channels interactions

The in silico approach presented in the previous sections was designedto qualitatively mimic the field potential acquired with MEA measurements(see Fig. 13), by taking into account a certain amount of variability. Ourpurpose is now to introduce in the model the action of compounds on ionchannels. The modeling of drug-channel interactions has been the object ofseveral studies (see e.g. [16, 27]). Various concepts have been introduced 1)pore block action: the flow of ions is inhibited by the drug binding with acontinuously accessible channel receptor; 2) modulated and guarded receptortheories: the drug access to the binding sites is restricted due to the channelconformation during the AP cycle; 3) allosteric effectors : a drug binding toa protein changes its activity and also activates conformational changes inits dynamics. In the present study, the pore block model is used because itdoes not require too many parameters and because it proved to be able toreproduce the relevant phenomena. The pore block model is implementedwith the “conductance-block” formulation [28, 29, 15, 30]. The conductanceof the targeted channel is reduced by a scaling factor in the following way:

gs = gcontrol,s

[1 +

([D]

IC50

)n ]−1, (8)

where gcontrol,s is the drug-free maximal conductance of channel s, the IC50

value of the drug is the drug concentration at which a 50% reduction of thespecific channel peak current is observed and [D] is the drug concentration.The Hill coefficient n will be assumed to be equal to 1.

3. Results

In this section, we first present the MEA signals given by our simulationand the impact of the modeling choices presented in subsection 2.2 to handleheterogeneity and variability. Next, in the second part of this section, weinvestigate the influence of drugs on numerical MEA signals and compare

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them to experimental data. All in silico and in vitro signals that will bepresented below are obtained without introducing any stimulation current.The firing occurs because of the pacemaker behavior of the cells, in vitro andin silico.

3.1. MEA signals simulation

Figure 7: Field potentials measured by the 9 electrodes: comparison between experimentaland simulation signals, obtained with the phenotype heterogeneity model.

To start with, we consider an heterogeneous media with two differentphenotypes as explained in Section 2.2.2. In Fig. 7, the results providedby our model (red lines) can be compared with experimental signals (bluelines). We observe that the depolarization is sharper in the simulations thanin the experiments and that the shapes of the FP during the plateau phaseexhibit significant differences. This motivates the use of the rescaling strat-egy, presented in Section 2.2.3. The results obtained with the rescaling arecompared with the experimental measurements in Fig. 8. The simulationresults (red lines) are now closer to the measured signals (blue lines). Evenif polarity differences remain for some electrodes, the agreement is very goodfor electrodes 1, 2, 3 and 5. Globally, a comparison with Fig. 7 shows thatthe experimental measurements are better reproduced in the present case,especially in the depolarization and in the plateau phases.

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Figure 8: Field potentials measured by the 9 electrodes: comparison between experimentaland simulation signals, obtained with the transmembrane rescaling model (all cells areventricular-like).

In Fig. 9(b) we present the simulated FP signals obtained with the rescal-ing procedure, which can be compared to those obtained without the rescalingprocedure (Fig. 3). In Fig. 9(a), we show the corresponding action potential(AP) traces averaged over the electrodes. One could see that the magnitudeof the transmembrane potential in the plateau phase is gradually rescaledfrom the left bottom to the right top corner. This gradation is due to theelectrotonic effect. In Fig. 9(d) (respectively, Fig. 9(c)), we present thesimulated FPs (respectively, APs) obtained when introducing only a pheno-type heterogeneity. The repartition of cells phenotypes follows the examplein Fig. 6, where in Ω1 we use ventricular model and in the domain Ω2, weuse atrial cells model. One could see in Fig. 9(c) a gradation in the APduration from the top right representing atrial phenotype to the bottomleft corners representing ventricular phenotype. Also this result can be ex-plained by the electrotonic effect. We observe that the rescaling allows tohave numerical results closer to the experimental curves presented in Fig. 4.The level of heterogeneity is then quantified in the box plots presented ofFig. 10: the magnitudes of the repolarization peak (Fig. 10(a)) and of thedepolarization-repolarization interval (Fig. 10(b)) show a significantly higherstandard deviation when the rescaling strategy is introduced in the model.

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(a) Action potential (b) Field potential

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(d) Field potential

Figure 9: Simulated transmembrane and field potentials over the 9 electrodes forventricular-like hiPSC-CMs with the rescaling procedure presented in Section 2.2.3 (top).Simulated transmembrane and field potentials over the 9 electrodes using phenotype het-erogeneity (bottom).

In the absence of rescaling (Fig. 3) the tissue is stimulated at the bottom-left corner with Istim = 150 µA cm−2 for 1 ms to trigger the propagation.In all these simulation, we have considered a clustered configuration (as in-troduced in Section 2.2.4). Let us now compare the results obtained withthe clustered and scattered repartitions of cells. In Fig. 11 and Fig. 12, acomparison of the results obtained with these two arrangements is shown:the clustered configuration produces a higher level of variability of the FPshapes and of the repolarization magnitude than the scattered one. This lastconfiguration tends to flatten the effects of heterogeneity. These resultsare in agreement with experimental observations, since the differentiationbetween cells is distributed in a sort of clustered manner and also neighbour-

16

Experiment Sim. Hetero Sim. Homo

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Experiment Sim. Hetero Sim. Homo-10

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(b) plateau magnitude

Figure 10: Effect of the rescaling heterogeneity on the plateau and repolarisation peakamplitudes of the field potential: Experimental data (first box), simulation with hetero-geneity (second box) and simulation without heterogeneity (third box). Y-axis refers tovoltage, values are in mV.

ing cells have influence on each other [6]. Finally, to mimic the variabilityobserved in the experiments and to generate several scenarios, we follow thestrategy explained in Section 2.2.5 which mixes the two previous approachesby introducing two phenotypes and differences in the AP amplitude. Six dif-ferent configurations are implemented by changing the ratio and the spatialarrangement of the subdomains Ω1 and Ω2. This allows to generate 54 signalsthat will be used for the statistics in the next subsection. In Fig. 13, the re-sults obtained with this procedure are shown. A visual inspection shows thatthe experimental variability of amplitude, frequency, shape and duration ofthe signals seems to be qualitatively well reproduced by these computations.In all the simulations where heterogeneities are introduced (by phenotype orby AP rescaling), we did not introduce any stimulation.

3.2. Assessment of the hiPSC-CMs/MEA/Drug model

In this section, results for different compounds are presented, commentedand compared with experimental observations. The experiments are per-formed with a 6-well MEA, all data are provided by Janssen Pharmaceuti-cals, Inc., and post-processed by Notocord R©. A set of 54 in silico signals isgenerated as explained right above in order to compute some statistics andto assess that the general effects of the specific drug are well reproduced bythe model. In the experimental data, we select from the 54 experimental

17

time (s)0 0.5 1 1.5

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20Electrode 0Electrode 1Electrode 2Electrode 3Electrode 4Electrode 5Electrode 6Electrode 7Electrode 8

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20Electrode 0Electrode 1Electrode 2Electrode 3Electrode 4Electrode 5Electrode 6Electrode 7Electrode 8

(b) scattered configuration

Figure 11: Field potential shapes obtained with F = 20%, with two different spatialarrangements (the black part is Ω2): on the left results for a “clustered configuration”, onthe right results for a “scattered configuration”.

(a) 10 clustered simulations (b) 10 scattered simulations

Figure 12: Repolarization magnitudes of the field potential collected by a single electrodefor 10 clustered simulations (left) and 10 scattered simulations (right). All results obtainedwith F = 20%.

signals those which are clean enough for extracting the different biomarkers.For the sake of clarity, the measurements and the simulations are presentedfor only one electrode. Figures containing the traces of the field potentialfor the 9 electrodes with multiple heart beats for both in vitro and in silicoexperiments are provided in the supplementary material.

3.2.1. Mexiletine

The effects of mexiletine on hiPSC-CMs are the blocks of the sodium andof the L-type calcium currents with IC50,INa

= 106.25µM and IC50,ICaL=

75µM [31]. Therefore this compound has an impact mainly on the depolar-izing phase of cells, as can be observed in the measurements of Fig. 14(a).The same dose-dependent effects are observed in both experiments and sim-

18

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Figure 13: Field potentials obtained with the phenotype heterogeneity model togetherwith the rescaling of the ventricular-like VM . 6 heterogeneity cases: change of the domainsplitting and of the rescaling parameters c1 and c2 inside the physiological range.

This is a quantification of which fraction of the “control amplitude” is ob-tained with a certain dose. The mean values of our simulations confirmthat the general e↵ect of mexiletine is well reproduced: the higher the drugconcentration the smaller the absolute and relative amplitudes. The statis-tics results on simulations and on experiments are comparable, especiallythe relative ones. The di↵erence in control conditions between simulations(8.6241 ± 2.0071) and experiments (1.7425 ± 0.6374) might be due to animperfect modeling of the electrodes. But rather that an absolute value,the important information is that the general trend is well captured by the

(a) Experiments (b) Simulations

Figure 14: Comparison between control conditions and 50µM and 100µM of mexiletine forone beat: experimental measurements (a) and simulations results (b).

18

Figure 13: Field potentials obtained with the phenotype heterogeneity model togetherwith the rescaling of the ventricular-like VM . 6 heterogeneity cases: change of the domainsplitting and of the rescaling parameters c1 and c2 inside the physiological range.

ulations (see the comparison of one beat in Fig. 14: blue lines correspondto control conditions, red lines to 50µM and black lines to 100µM). The re-duction of the depolarization amplitude is well reproduced. The resultsobtained with a simulation of 4s are shown in Fig. 15. These curves corre-spond to one electrode and one configuration of cells. The frequency of firingis consistently reduced in presence of mexiletine. The same effect was ob-served in all the other studied configurations. In the paper by Harris et al. [9],it is observed that the beating is stopped in 3 out of 5 plates, with 30µMof mexiletine. Nevertheless, the present experimental data do not show thisbehavior. In order to get a more general assessment, we have reported inTable 2(a)-(b) the mean and standard deviation of the effect on the depolar-ization for six simulated wells (54 signals) and for the six experimental wells.

19

(a) Experiments (b) Simulations

Figure 14: Comparison of the field potential between control conditions and 50µM and100µM of mexiletine for one beat: experimental measurements (a) and simulations results(b).

Figure 15: Comparison of the field potential between control conditions and 50µM and100µM of mexiletine for 4 seconds simulation.

For the experimental signals, a few electrodes with a too low signal to noiseratio were removed. The amplitude of the depolarization wave is computedas the absolute difference between the maximum and the minimum of theFP during depolarization. The relative depolarization amplitude (amplitudeof the signal with the drug relative to the amplitude in control conditions)is computed as

RelAmpli,j =Ampli,jdoseAmpli,jcontrol

for i = ith well, j = jth electrode. (9)

This is a quantification of which fraction of the “control amplitude” is ob-tained with a certain dose. The mean values of our simulations confirmthat the general effect of mexiletine is well reproduced: the higher the drug

20

concentration the smaller the absolute and relative amplitudes. The statis-

(a) Experiments

Depol. ampl Mean Std devControl 1.7425 0.637450µM mex 1.2104 0.6698100µM mex 0.7228 0.3438Depol. relative ampl50µM mex 0.6841 0.2223100µM mex 0.4392 0.1729

(b) Simulations

Depol. ampl Mean Std devControl 8.6241 2.007150µM mex 3.8681 1.0106100µM mex 2.8364 0.9758Depol. relative ampl50µM mex 0.4525 0.0795100µM mex 0.3300 0.0800

(c) Experiments

Repol. peak Mean SDControl 0.1980 0.2650µM mex 0.1800 0.24100µM mex 0.1380 0.15Repol. peak rel. amp. Mean SD50µM mex 0.8239 0.2960100µM mex 0.6293 0.3605

(d) Simulations

Repol. peak. Mean SDControl 0.36 0.103150µM mex 0.26 0.1129100µM mex 0.1780 0.1234Repol. peak rel. amp. Mean SD50µM mex 0.6988 0.1652100µM mex 0.4922 0.1774

Table 2: Statistics computed on simulated and experimental signals to assess the effectof mexiletine. Absolute values of mean and standard deviation of the depolarizationamplitude and repolarization peak amplitude in control conditions and with 50µM and100µM.

tics results on simulations and on experiments are comparable, especiallythe relative ones. The difference in control conditions between simulations(8.6241± 2.0071) and experiments (1.7425± 0.6374) might be due to an im-perfect modeling of the electrodes. But rather that an absolute value, theimportant information is that the general trend is well captured by the model.In Table 2(c)-(d), we compare the statistics on the repolarization peak am-plitude of experimental and simulated signals: a reduction is observed inboth in vitro and in silico, but more pronounced in the latter. Regardingthe repolarization time, we report in Table 3.2.1 (a)-(b) statistics on the re-polarization time (RT) with and without rate correction. Corrections followBazett’s formula. We observe that, without rate correction RT intervals areincrease when introducing each drug dose. But in experiment, this effect ismore pronounced with 50µM than with 100µM, which is not the case in the insilico simulations. When looking at the rate corrected repolarization times,we observe the same effect as without rate correction in the experimentaldata. But in the in silico results, we observe that the rate corrected RTsdecrease with respect to the drug dose.

21

(a) Experiments

RT Mean SDControl 0.1714 0.024250µM mex 0.2096 0.0291100µM mex 0.1826 0.0123RT (rate corrected). Mean SDControl 0.1768 0.023250µM mex 0.2350 0.0359100µM mex 0.2053 0.0101

(b) Simulations

RT Mean SDControl 0.3403 0.027650µM mex 0.3555 0.0276100µM mex 0.3965 0.0321RT (rate corrected). Mean SDControl 0.3582 0.023850µM mex 0.3295 0.0224100µM mex 0.3222 0.0256

Table 3: Statistics computed on simulated and experimental signals to assess the effectof mexiletine. Repolarization time with and without rate correction in control conditionsand for 50µM and 100µM drug doses.

3.2.2. Dofetilide

Dofetilide is known to block the IKr channel with IC50,IKr= 5nM [29].

This induces a delay and a reduction of the peak amplitude in the repolar-ization phase. In Fig. 16, blue lines correspond to control conditions, redlines to 10nM and black lines to 50nM. In both experimental and simulationcurves, we can notice the same dose-dependent delay of the repolarizationwave and also a (slight) reduction of the peak amplitude of the repolarization.In Table 4(c)-(d), we show the effect on the FP repolarization for different

heterogeneity configurations. The reduction of the repolarization maximalamplitude (absolute values and values relative to control conditions) showsvery high standard deviations. It is therefore difficult to draw a conclusionon this aspect. The delay of repolarization for a given dose is quantified asthe difference between the instant of the repolarization peak in presence andabsence of dofetilide:

TDelayi,j = timei,jrepol,dose−timei,jrepol,control for i = ith well, j = jth electrode.(10)

We compute the rate correction of the time delay TDelayc using Bazett’sformula as follows

TDelayci,j =

timei,jrepol,dose√RRi,j

dose

−timei,jrepol,control√

RRi,jcontrol

, for i = ith well, j = jth electrode.

(11)This delay, causing an increase of the signal duration, is well reproduced inall our simulations, as confirmed by the computed statistics in Table 4(e).Repolarization delay statistics in the experimental data are reported in Table

22

(a) Experiments (b) Simulations

(c) Experiments (d) Simulations

Figure 16: Comparison between control conditions and 10nM and 50nM of dofetilide forone beat: experimental measurements (a) and simulations results (b).

4(f). We observe that the delay periods with and without rate correction areless pronounced in the experimental data then they are in the in silico results.

In Figure 16(c) and 16(d), we show multiple beats: one could see thatdofetilide reduces the spike amplitude. This effect is clearly seen in in vitroexperiments, as shown also by Table 4(a). The same effect is present also insilico, but it is less pronounced. As a consequence, we also see that dofetilidereduces beating rate of the stem cells. In fact, the cycle length in the simu-lated results is 0.903±0.028 s (respectively, 1.114±0.043 s, 1.349±0.037 s) forthe control (respectively, 10nM, 50nM) case. These unexpected effects havebeen reported in the case of in vitro experiments in the work by Qu and Var-gas (2015) [32]. More figures on the effect of dofetilide on the nine electrodesextracted from one well are provided in the supplementary material.

3.2.3. BayK

Bay K8644 is an ICaL agonist, namely a drug that activates the L-typecalcium channels by increasing the current in a dose-dependent manner. This

23

(a) Experiments

Depol. rel. amp. Mean SD10nM dofetilide 0.817 0.19850nM dofetilide 0.389 0.219

(b) Simulations

Depol. rel. amp. Mean SD10nM dofetilide 1.016 0.1050nM dofetilide 0.949 0.119

(c) Experiments

Repol. peak amplitude Mean SDControl 0.0986 0.114310nM dofetilide 0.0906 0.106650nM dofetilide 0.0644 0.0733Repol. peak rel amp. Mean SD10nM dofetilide 0.9367 0.108350nM dofetilide 0.8495 0.1642

(d) Simulations

Repol. peak amplitude Mean SDControl 0.3631 0.260110nM dofetilide 0.3272 0.222450nM dofetilide 0.3223 0.2341Repol. peak rel amp. Mean SD10nM dofetilide 0.9048 0.084850nM dofetilide 0.7089 0.1701

(e) Simulations

Repol. wave time delay Mean SD Mean (rate corrected) SD (rate corrected)10nM dofetilide 0.1579 0.0822 0.1311 0.084850nM dofetilide 0.2863 0.0897 0.2126 0.0844

(f) Experiment

Repol. wave time delay Mean SD Mean (rate corrected) SD (rate corrected)10nM dofetilide 0.043 0.035 0.068 0.04850nM dofetilide 0.081 0.057 0.055 0.024

Table 4: Comparison of the effect of dofetilide on the field potential for both in silicoand in vitro experiments. The comparison is evaluated on repolarization peak amplitude,depolarization amplitude and repolarization wave delay for doses 10 nM and 50 nM.

action evidently cannot be modeled with the conductance block formulation,because the conductance needs to be increased. The following relation modelsthe effect of an agonist on a generic channel s [33]:

gAs = gs

(1 +

αDn

KnA +Dn

). (12)

gAs is the conductance modified with the agonist, depending on the conduc-tance in control conditions gs, on the drug dose D, on the Hill coefficient n,on α (the maximal relative increase of the channel current induced by theagonist) and on the dissociation constant KA. In Fig. 17, both the experi-mental and the simulation signals clearly show the expected prolongation ofthe plateau when BayK is added. The two doses of 1µM and 5µM producealmost the same effect (signals almost superposed), because they are close tothe threshold of concentration after which the effect is at its maximum. Thisbehavior is present in both experiments and simulations. The general effect

24

(a) Experiments (b) Simulations

Figure 17: Comparison between control conditions and 1µM and 5µM of BayK for onebeat: experimental measurements and simulations results.

is always reproduced, as observed when running simulations for six differentconfigurations. The plateau duration can be quantified as

P i,jduration = ti,jS − ti,jrepol for i = ith well, j = jth electrode, (13)

ti,jS being the time of the end of the depolarization and trepol the peak of therepolarization time. Table 5(a) (respectively, (b)) shows the mean values andthe standard deviations of the plateau duration for the in silico (respectively,in vitro) signals for each drug dose. We observe that when adding BayK,the mean value increases dose-dependently. For the two doses, the meanvalues are very close for the reason explained above when commenting thesuperposed curved of Fig. 17. In Table 5(c)-(d) the effect of BayK on theT-peak magnitude is presented. We observe that this biomarker is decreasedin the experimental data, whereas it is increased in simulation: for a dose of5µM, the mean of the relative magnitude of the T-peak is 0.76 in experimentsand 1.34 in simulations.

3.2.4. Ivabradine

Ivabradine is a compound which blocks the funny current If with IC50 =2.1µM [34]. If is only present in pacemaker cells and is able to give rise toinstability during the resting potential phase. Therefore, the general effectof ivabradine is a decrease of the beating frequency, which can be observedon the measurements plotted in Fig. 18(a). In Fig. 18(b), the simulationsresults obtained with a specific configuration on one electrode are shown. Inboth experimental and computed signals, the frequency is slowed down as theconcentration of ivabradine is increased. The drug does not alter the general

25

(a) Simulations

Plateau duration Mean SD Mean (rate corrected) SD (rate corrected)Control 0.1166 0.0583 0.1240 0.0621µM BayK 0.1770 0.0609 0.1844 0.06345µM BayK 0.1802 0.0609 0.1858 0.0628

(b) Experiment

Plateau duration Mean SD Mean (rate corrected) SD (rate corrected)Control 0.1513 0.0152 0.1106 0.07241µM BayK 0.1702 0.0264 0.2419 0.03875µM BayK 0.1855 0.0146 0.2616 0.0226

(c) Experiments

Repol. peak amplitude Mean SDControl 0.3675 0.21931µM BayK 0.3100 0.19775µM BayK 0.2963 0.2186Repol. peak rel amp. Mean SD1µM BayK 0.8315 0.08155µM BayK 0.7670 0.1031

(d) Simulations

Repol. peak amp. Mean SDControl 0.4373 0.17111µM BayK 0.5775 0.19795µM BayK 0.5777 0.1976Repol. peak rel. amp. Mean SD1µM BayK 1.3489 0.16785µM BayK 1.3499 0.1684

Table 5: Comparison of the effect of BayK on the field potential for both in silico and invitro experiments. The comparison is evaluated on repolarization peak amplitude and onthe plateau duration for doses 1µM and 5µM.

shape of the FP. In all the studied configurations, the computational modelgives the expected effects, even though the delay is lower than in experiments.In Fig. 19(a) (respectively, (b)), we show how ivabradine prolongs the cyclelength in the experimental (respectively, simulated) case. We see that theeffect is much more pronounced in the experiments than it is in the in silicomodel.

3.2.5. Bepridil

As a last example, we reproduce the effects of bepridil, a compound thatblocks multiple channels. The main action is on IKr, but for high doses italso affects the sodium channel INa and the L-type calcium current ICaL:the IC50 values for the three channels are respectively 33nM, 3.7µM and211nM [29]. In Fig. 20, the doses of 1µM and 5µM are analyzed: at theseconcentrations, all the three channels are affected and the whole signal isdose-dependently changing. In our results in Fig. 20(b), the repolarizationwave almost disappears, the depolarization is enlarged and its amplitudedecreases with the drug dose. The duration is slightly increased due to thefact that bepridil affects more IKr than ICaL. The same effects are alsopresent in the experimental signals of Fig. 20(a), but less pronounced: the

26

(a) Experiments (b) Simulations

Figure 18: Comparison between control conditions and 5µM and 10µM of ivabradine for4 seconds: experimental measurements and simulations results.

amplitude of the depolarization is reduced but the wave is not enlarged andthe peak of the repolarization is delayed but does not disappear. This canbe explained by the fact that the IC50 values that we are using are not fittedon the case of hiPSC-CMs but on guinea pig CMs. In the case of stem cells,for bepridil, we expect that higher IC50 values would better reproduce theexperimental signals. In Table 6, we quantify the action of bepridil on the

(a) Experiments

Depol. ampl Mean Std devControl 1.9663 1.04521µM 1.6432 0.74285µM 1.2977 0.6707Depol. relative ampl1µM 0.8771 0.22235µM 0.6952 0.3200

(b) Simulations

Depol. ampl Mean Std devControl 8.6241 2.00711µM bep 2.8250 1.07645µM bep 1.3844 0.5712Depol. relative ampl1µM bep 0.3337 0.09625µM bep 0.1599 0.0495

Table 6: Statistics computed on simulated and experimental signals to assess the effect ofbepridil. Absolute values of mean and standard deviation of the depolarization amplitudein control conditions and with a dose of 1µM and 5µM. Relative values computed as inrelation (9).

depolarization wave for the six simulations cases and the six wells, as donefor the case of mexiletine. The mean values confirm that the reduction of thedepolarization amplitude is reproduced by the simulations. Regarding theexperimental measurements, the standard deviations are very high, becausethis set of data are noisy. As observed above, the computation results showa more pronounced effect of the compound than the experiments.

27

Control 5uM 10uM

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Figure 19: Effect of Ivabradine on the activation rate: Comparison between control con-ditions and 5µM and 10µM, experimental measurements (left) and simulations results(right).

4. Discussion and conclusion

The main objective of the study was to introduce a mathematical modelof MEA measurements on hiPSC-CMs. After its mathematical derivation,the model has been tested with several simulations and compared with exper-imental measurements. Many modelling hypotheses were justified by litera-ture studies and experimental observations. Based on the works [6, 9, 4, 5],two different phenotypes have been introduced in the model and a variabilityin the action potential amplitudes has been taken into account. We do nothave any information on how the cells are seeded in the monolayer prepara-tion. According to the collected signals and to the simulation obtained withthe mathematical model that we use, our hypothesis is that phenotypes areorganized in a clustered manner.

Obtaining in silico signals that exactly match a specific experiment isvery difficult and not necessarily desirable. The difficulty comes from vari-ous experimental uncertainties. However, the model was able to qualitativelyreproduce the main features observed in the experiments. This proved to besufficient to detect the effect of drugs, which were studied with the pore blockmodel. MEA pharmaceutical experiments were simulated for five differentcompounds. Again, the assessment was not done by a point to point compar-ison, which would not make sense given the variability of the experiments.

28

(a) Experiments (b) Simulations

Figure 20: Comparison between control conditions and 1µM and 5µM of bepridil for onebeat: experimental measurements and simulations results.

Instead, it was performed by considering average trends of biomarkers. ForMexiletine, our study shows a good agreement in terms of depolarization andrepolarization peak amplitudes between in vitro and in silico results. On thecontrary, the comparison on the repolarization times shows that the effectof Mexiletine of the RT without rate correction is not monotonous with thevalue of the drug dose in the in vitro measurements, whereas it is in the insilico data. However, when introducing rate correction we obtain this non-monotonicity for both in silico in vitro signals, but still more pronounced inexperiments than it is in simulations. For dofetilide, both in silico and invitro models show a repolarization delay and a reduction of the repolariza-tion peak amplitude with the drug doses. However, the effect of dofetilide onthe depolarization amplitude was very small in simulation compared to whatit is in experiments. A high effect of dofetilide on the depolarization is notexpected because it is not supposed to affect the sodium current. This unex-pected effect has been reported in the experimental study by Qu and Vargas(2015) [32] where for high doses of dofetilide early after depolarization wavesappear and may consequently alter the sodium current in the depolarization.This could explain the reduction of the depolarization wave magnitude. Moreinvestigations on both in vitro and in silico experiments are needed in orderto clarify this issue. For BayK, we obtained a good agreement between sim-ulation and experiment in terms of repolarization delay due to an increaseof the plateau duration. However, both models provide do not agree on theeffect of BayK on the depolarization magnitude. While in experiments we ob-serve a decrease of this biomarker, in the simulation we observe a pronouncedincrease of the depolarization magnitude with the drug dose. The reason of

29

this contradictory effect is not clear, it could be related to the formulation ofthe calcium current in the Paci et al [18] model. Again more investigationsare needed in order to elucidate this question. For bepridil, both modelsare in agreement in the effect of the drug on the reduction of depolarizationamplitude which is more pronounced in the in silico model. For Ivabradineboth models are also in agreement its effect on prolonging cycle length witha higher effect in the in vitro model. Even if for some compounds the effectwas more pronounced in the simulations than in the experiments, the in sil-ico model generally gave results in good agreement with the experiments.Many aspects of the modelling approach could be improved.

• Some parameters used for the bidomain equations such as the intra-cellular and extra-cellular conductivities are not based on experimentalvalues. Their values are less than the conductivities in the cardiactissue. This is in agreement with the findings of Blazeski et. al [6],where it has been shown that for hIPSC-CM the conduction velocity(CV) is much slower than in a normal human heart. However, thiscould be related to other factors that are not taken into account in ourmodel, such as gap junctions. The values that we introduced have beenchosen to fit the CV in the in vitro experiment.

• The heterogeneity of the hiPSC-CMs preparations has been modeledin a somehow arbitrary way, with mainly qualitative arguments. Evenif an averaging procedure allows to limit the consequences of this arbi-trariness, it would be more satisfactory to rely on a better experimentalcharacterization of the phenotypes repartition in the monolayer model.

• The ionic model is not necessarily well adapted to the hiPSC-CMs usedin the experiments, even if it was designed for stem cells. For instance,there is no description of late sodium current in the Paci model and thislimitation moderates the results obtained on the effect of mexiletine onthe field potential.

• When computing the different biomarkers quantities on the QRS andthe repolarization wave, we only perform rate variability correctionswhen computing time intervals or delays. For the magnitude relatedbiomarkers, the only correction that we introduce is to compute relativequantities with respect to the control case.

30

• The parameters used for the drug model, like the IC50 values, do notnecessarily correspond to the parameters of hiPSC-CMs.

In spite of all these limitations, this multiscale approach, which com-bines physiologically detailed ionic models with the bidomain equations anda model of a MEA device, is able to reproduce the correct trends of the effectof drugs. It might therefore be a valuable tool to analyze the signals acquiredby MEAs: given a series of measurements corresponding to different doses ofa compound, parameter identification algorithms could be used to automat-ically identify which channels were affected. This is the object of an ongoingwork.

5. Acknowledgments

This work was partially supported by the French National Agency of Re-search through the grant ANR-13-LAB1-0007 (LabCom “CardioXcomp”).We would like to thank Janssen Pharmaceutica NV for providing us withthe raw data, and David Labarre, Fabien Raphel and Christophe Bleunvenfor many fruitful discussions and for their assistance to deal with the exper-imental data.

6. References

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